Ukrainian Mathematical Journal

, Volume 51, Issue 11, pp 1749–1763 | Cite as

Approximation of locally integrable functions on the real line

  • A. I. Stepanets
  • Wang Kunyang
  • Zhang Xirong
Article
  • 26 Downloads

Abstract

We introduce the notion of generalized\(\bar \psi \)-derivatives for functions locally integrable on the real axis and investigate problems of approximation of the classes of functions determined by these derivatives with the use of entire functions of exponential type.

Keywords

Fourier Series Entire Function Periodic Function Real Axis Integrable Function 

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References

  1. 1.
    A. I. Stepanets, “Approximation in spaces of locally integrable functions,”Ukr. Mat. Zh.,46, No. 5, 638–670 (1994).CrossRefMathSciNetGoogle Scholar
  2. 2.
    A. I. Stepanets, “Classification of periodic functions and the rate of convergence of their Fourier series,”Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 1, 101–136 (1986).MathSciNetGoogle Scholar
  3. 3.
    A. I. Stepanets, “On the Lebesgue inequality on the classes of (ψ, β)-differentiable functions,”Ukr. Mat. Zh.,41, No. 5, 449–510 (1989).Google Scholar
  4. 4.
    A. I. Stepanets, “Deviations of Fourier sums on classes of entire functions,”Ukr. Mat. Zh.,41, No. 6, 783–789 (1989).CrossRefMathSciNetGoogle Scholar
  5. 5.
    A. I. Stepanets,Classification and Approximation of Periodic Functions, Kluwer, Dordrecht (1995).MATHGoogle Scholar
  6. 6.
    A. I. Stepanets, “Convergence rate of Fourier series on the classes of\(\bar \psi \)-integrals,”Ukr. Mat. Zh.,49, No. 8, 1069–1114 (1997).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    A. I. Stepanets, “Approximation of\(\bar \psi \)-integrals of periodic functions by Fourier sums (low smoothness),”Ukr. Mat. Zh.,50, No. 2, 274–291 (1998).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    N. I. Akhiezer,Lectures in Approximation Theory [in Russian], Nauka, Moscow (1965).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. I. Stepanets
    • 1
  • Wang Kunyang
    • 2
  • Zhang Xirong
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Normal UniversityBeijingChina

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